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Formula Sheet - Differential Equations Formula Sheet x = e...

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Differential Equations Formula Sheet ( 29 m T T k dt dT - = ( 29 t r e P K P K P t P - - + = 0 0 0 ) ( 0 2 2 2 = + x dt x d ϖ , m k / 2 = ϖ , t c t c t x ϖ ϖ sin cos ) ( 2 1 + = , ϖ π / 2 = T , π ϖ 2 / / 1 = = T f ( 29 φ ϖ ϖ ϖ + = + = t A t c t c t x sin sin cos ) ( 2 1 , 2 2 2 1 c c A + = , A c 1 sin = φ , A c 2 cos = φ 0 2 2 2 2 = + + x dt dx dt x d ϖ λ , m β λ = 2 , m k = 2 ϖ 0 2 2 - ϖ λ , + = - - - - t e c e c e t x t t 2 2 2 2 2 1 ) ( ϖ λ ϖ λ λ 0 2 2 = - ϖ λ , ( 29 t c c e t x t 2 1 ) ( + = - λ 0 2 2 < - ϖ λ , ( 29 t c t c e t x t 2 2 2 2 2 1 sin cos ) ( λ ϖ λ ϖ λ - + - = - ) ( 4 4 x w dx y d EI = n n D x x x - 1 2 , , , , 1 ( 29 n x n x x x D e x e x xe e α α α α α - - 1 2 , , , , ( 29 [ ] n x n x x x x n x x x D D x e x x e x x xe x e x e x x e x x xe x e 2 2 2 1 2 1 2 2 sin , , sin , sin , sin cos , , cos , cos , cos β α α β β β β β β β β α α α α α α α α + + - - - ( 29 ( 29 [ ] x c x c x y x x c x x c x x c x c y x c x c y k m k m m m m m ln sin ln cos ) (ln ) (ln ln 2 1 1 2 3 2 1 2 1 1 1 1 1 2
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